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Necessary and sufficient conditions for oscillations of delay differential inequalities

Published online by Cambridge University Press:  17 April 2009


Jurang Yan
Affiliation:
Department of Mathematics, Shanzi University, Taiyuan, Shanxi, People's Republic of China.

Abstract

A necessary and sufficient condition is obtained for a first order linear delay differential inequality to be oscillatory. Our main result improves and extends some known results.


Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Koplatadze, R.G. and Chanturia, T.A., ‘On oscillatory and monotonic solutions of first-order differential equations with retarded arguments’, Russian, Differensial'nye Urauneniya 8 (1982), 14631465.Google Scholar
[2]Ladas, G., ‘Sharp conditions for oscillations caused by delays’, App. Anal. 9 (1979), 9398.CrossRefGoogle Scholar
[3]Ladas, G. and Stavroulakis, I.P., ‘On delay differential inequalities of first order’, Funkcial Ekvac. 25 (1982), 105113.Google Scholar
[4]Yan, J., ‘Oscillation of solutions of first order delay differential equations’, Nonlinear Anal. 11 (1987), 12791287.CrossRefGoogle Scholar
[5]Zhang, B.G., ‘A survey of the oscillation of solutions of first order differential equations with deviating argument’, Proc. International Conference on Trends in Nonlinear Analysis,Arlington,TXJune 12–22(1984).Google Scholar

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